Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T21:50:39.442Z Has data issue: false hasContentIssue false
  • English
  • Français

A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold

Published online by Cambridge University Press:  20 November 2018

Wei Zhao
Wei Zhao*
Affiliation:
Center of Mathematical Sciences, Zhejiang University, Hangzhou, China e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.

Keywords

53B4053C22Finsler manifoldclosed geodesicinjective radius
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 194 - 208
Copyright
Copyright © Canadian Mathematical Society 2014

References

[BC] Bácsό, S., Cheng, X., and Shen, Z., Curvature properties of -metrics. In: Finsler geometry, Sapporo 2005, Advanced Studies in Pure Mathematics, 48, Math. Soc. Japan, Tokyo, 2007, pp. 73–110.Google Scholar
[BCS] Bao, D., Chern, S. S., and Shen, Z., An introduction to Riemann-Finsler geometry. Graduate Texts in Mathematics, 200, Springer-Verlag, New York, 2000.Google Scholar
[C] Chavel, I., Riemannian geometry. A modern introduction. Second ed., Cambridge Studies in Advanced Mathematics, 98, Cambridge University Press, Cambridge, 2006.Google Scholar
[Ch] Cheeger, J., Finiteness theorems for Riemannian manifolds. Amer. J. Math. 92 (1970), 61–74. http://dx.doi.org/10.2307/2373498 Google Scholar
[CS] Chern, S.-S. and Shen, Z., Riemann-Finsler geometry. Nankai Tracts in Mathematics, 6, World Scientific Publishing Co., Hackensack, NJ, 2005.Google Scholar
[E] Egloff, D., Uniform Finsler Hadamard manifolds. Ann. Inst. H. Poincaré Phys. Thér. 66 (1997), no. 3, 323–357.Google Scholar
[HK] Heintze, E. and Karcher, H., A general comparison theorem with applications to volume estimates forsubmanifolds.Ann. Sci. Ecole Norm. Sup. (4) 11 (1978), no. 4,451–470.Google Scholar
[K] Klingerberg, W., Contributions to Riemannian geometry in the large. Ann. of Math. (2) 69 (1959), 654–666. http://dx.doi.org/10.2307/1970029 Google Scholar
[Ru] Rund, H., The theory of subspaces of a Finsler space. I. Math. Z. 56 (1952), 363–375. http://dx.doi.org/10.1007/BF01686755 Google Scholar
[S] Shen, Z., Lectures on Finsler geometry. World Scientific Publishing, Singapore, 2001.Google Scholar
[W] Y.Wu, B., Volume form and its applications in Finsler geometry. Publ. Math. Debrecen 78 (2011), no. 3–4, 723–741. http://dx.doi.org/10.5486/PMD.2011.4998 Google Scholar